Question

Consider the cubic unit cell of an ionic solid as given in the figure. With respect to this, select the correct statement(s).

• A. Formula of the solid is $A{B}_2$.
• B. Formula of the solid is $A{B}_3$.
• C. Coordination number of $A$ is $6$.
• D. Coordination number of $A$ is $4$.

Answer 1

Answer: (B), (C)

The correct options are
B Coordination number of $A$ is $6$.
C Formula of the solid is $A{B}_3$.

It can be seen from the figure that $A$ atoms are present at the corners of a cube.

There are $8A$ atoms in one unit cell and each one contributes one eight to the unit cell.

Thus, the number of $A$ atoms in one unit cell is $8\times \frac{1}{8}=1$

$B$ atoms are present at the edge-centres of the cube.

There are $12B$ atoms in one unit cell and each one contributes one fourth to the unit cell.

Thus, the number of $B$ atoms in one unit celll is $12\times \frac{1}{4}=3$

Hence, the formula of the solid is $A{B}_3$.

The coordination number of $A$ is $6$, as each $A$ is surrounded by $6B$ atoms.

Thus, the statement $A$ and $D$ are incorrect, whereas statements $B$ and $C$ are correct.